In this undated photo provided by the Zwick family, Carol Hollar-Zwick, left, and her son show a box of supplies found in an underground fallout shelter in the back yard of their Neenah, Wis. home.

What they didn’t know — and wouldn’t discover until they ventured into the shelter more than a decade later — was the bunker was fully stocked with food and survival supplies from 1960 by the previous homeowner.

“We assumed it was just this empty space,” Hollar-Zwick said.

When the Zwicks unlocked the heavy, metal hatch, they found watertight Army surplus boxes floating in 5 feet of...